Problem: A group of adults and kids went to see a movie. Tickets cost $$8.00$ each for adults and $$3.50$ each for kids, and the group paid $$52.00$ in total. There were $5$ fewer adults than kids in the group. Find the number of adults and kids in the group.
Solution: Let $x$ equal the number of adults and $y$ equal the number of kids. The system of equations is then: ${8x+3.5y = 52}$ ${x = y-5}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${y-5}$ for $x$ in the first equation. ${8}{(y-5)}{+ 3.5y = 52}$ Simplify and solve for $y$ $ 8y-40 + 3.5y = 52 $ $ 11.5y-40 = 52 $ $ 11.5y = 92 $ $ y = \dfrac{92}{11.5} $ ${y = 8}$ Now that you know ${y = 8}$ , plug it back into ${x = y-5}$ to find $x$ ${x = }{(8)}{ - 5}$ ${x = 3}$ You can also plug ${y = 8}$ into ${8x+3.5y = 52}$ and get the same answer for $x$ ${8x + 3.5}{(8)}{= 52}$ ${x = 3}$ There were $3$ adults and $8$ kids.